Besearches in the Theory and Calculus of Operations. 273 



the first carrying the body uniformly through space, the 

 second transmitting equal vibrations to surrounding sub- 

 stances, and the third finishing its career by splitting all 

 obstructions and rushing together in mutual annihilation 

 or equilibration. Translatory motion is finally destroyed 

 either by encountering immovable obstacles, or by the re- 

 sistance of the medium through which the body pursues 

 its way. The vibratory or calorific movements are reduced 

 to quiescence when their momentum has become uniformly 

 imparted to all the atoms enclosed within the extent of 

 transmission. The generated forces are annihilated ; but the 

 generating forces, the material substances themselves are 

 immanent, their effects alone perishing (phenomena are 

 transitory). 



15. Having shown how force can be developed from 

 solids, we may now introduce the condition of liquidity, in 

 which combination or union of different substances, and 

 decomposition or disunion of compound substances, are 

 operations that take the place of the liberation and equili- 

 bration of forces : composition of substances, the generating 

 forces themselves, instead of their generated forces only, 

 though necessarily involving the latter also. 



The smaller the difference, the easier the restoration to 

 harmony. When two vibrating cords, or the swinging pen- 

 dulums of two equal going clocks, are brought sufficiently 

 near together to feel each other's beats through the inter- 

 vening medium, provided their differences of oscillation 

 are small, they will gradually merge into unison ; the meet- 

 ing impulses successively tending to equality, because the 

 weaker gains what the stronger loses. When two chemical 

 substances are mixed in the liquid or gaseous state, they 

 combine into a neutral by first intention, provided their 

 atomical energies are in some commensurable relation to 

 one another, just like the combination of chords in the dia- 

 pason. If, however, two chemical energies are only near 

 Trans. 35 



